$A$ rope is used to lower a block of mass $M$ vertically by a distance $x$ with a constant downward acceleration of $\frac{g}{2}$. The work done by the rope on the block is:

$A$ galvanometer may be converted into an ammeter or a voltmeter. In which of the following cases will the resistance of the device so obtained be the largest?

Which of the following does not produce $NO_2$ gas with concentrated $HNO_3$?

For $k=1, 2, 3$, the box $B_k$ contains $k$ red balls and $(k+1)$ white balls. Let $P(B_1)=\frac{1}{2}$, $P(B_2)=\frac{1}{3}$, and $P(B_3)=\frac{1}{6}$. $A$ box is selected at random and a ball is drawn from it. If a red ball is drawn, then the probability that it has come from box $B_2$ is:

$A$ heavy nucleus at rest breaks into two fragments which fly off with velocities in the ratio $3: 1$. The ratio of radii of the fragments is

The area (in sq. units) of the region described by $\{(x,y): y^2 \le 2x \text{ and } y \ge 4x - 1\}$ is